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Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a newoptimization-via-compilationstrategy to scalably solve a certain class of such problems. In particular, we introduce a new intermediate representation (IR), binary decision diagrams weighted by a novel notion ofbranch-and-bound semiring, that enables a scalable branch-and-bound based optimization procedure. This IR automaticallyfactorizesproblems through program structure andprunessuboptimal values via a straightforward branch-and-bound style algorithm to find optima. Additionally, the IR is naturally amenable tostaged compilation, allowing the programmer to query for optima mid-compilation to inform further executions of the program. We showcase the effectiveness and flexibility of the IR by implementing two performant languages that both compile to it: dappl and pineappl. dappl is a functional language that solves maximum expected utility problems with first-class support for rewards, decision making, and conditioning. pineappl is an imperative language that performs exact probabilistic inference with support for nested marginal maximum a posteriori (MMAP) optimization via staging. 

As technical computing software, such as MATLAB and SciPy, has gained popularity, ecosystems of interdependent software solutions and communities have formed around these technologies.The development and maintenance of these technical computing ecosystems requires expertise in both software engineering and the underlying technical domain. The inherently interdisciplinary nature of these ecosystems presents unique challenges and opportunities that shape software development practices.Proof assistants, a type of technical computing software, aid users in the creation of formal proofs. In order to examine the influence of the underlying technical domain --- mathematics --- on the development of proof assistant ecosystems, we mined participant activity data from the code repositories and social channels of three popular proof assistants: Lean, Coq, Isabelle. Despite having a shared technical domain, we found little cross-pollination between contributors to the proof assistants. Additionally, we found that most long-term developers focused solely on technical work and did not participate in official social channels. We also found that proof assistant developers specialized into technical subfields. However, the proportion of specialists varied between ecosystems. We did not find evidence that these specialties contributed to fractures within the ecosystems. We discuss the implications of these results on the long-term health and sustainability of proof assistant ecosystems.This artifact contains the scripts and dataset that support an MSR 2024 article. 

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms of a specially chosen basis for the kernel of the maximal operator and employs a description of the Friedrichs extension due to Möller and Zettl.